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Reflection of moving shock wave over Prandtl–Meyer expansion waves

Published online by Cambridge University Press:  26 September 2025

Miao-Miao Wang Open the ORCID record for Miao-Miao Wang [Opens in a new window]  and
Zi-Niu Wu Open the ORCID record for Zi-Niu Wu [Opens in a new window]
Miao-Miao Wang*
Affiliation:
Department of Engineering Mechanics, Tsinghua University, Beijing 100084, PR China
Zi-Niu Wu*
Affiliation:
Department of Engineering Mechanics, Tsinghua University, Beijing 100084, PR China
*
Corresponding authors: Miao-Miao Wang, mmwang@mail.tsinghua.edu.cn; Zi-Niu Wu, ziniuwu@tsinghua.edu.cn
Corresponding authors: Miao-Miao Wang, mmwang@mail.tsinghua.edu.cn; Zi-Niu Wu, ziniuwu@tsinghua.edu.cn
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Abstract

This study examines the reflection of a rightward-moving shock (RMS) over expansion waves, dividing the reflection structure into three components. The first component analyses the pre- and post-interaction parts of the expansion waves, categorising primary flow patterns into four types with defined transition criteria, visualised through Mach contours. The second component investigates the curved perturbed shock. Through numerical simulations, the influence of increasing shock strength on the flow structures is displayed. A triple point forms for an RMS of the first family, and the Mach stem height increases with the increase of shock strength. When the RMS is strong enough, a vortex forms in the near-wall region, which acts like a wedge to distort the near-foot part of the RMS. The third component, the near-foot region, is analysed using a one-dimensional Riemann problem approach. The calculated wave speeds are used to mark waves in Mach contours for eight cases. The position of the waves indicates that the left-going shock for an RMS of the first family or the right-going shock for an RMS of the second family corresponds to the foot of the RMS. This can explain the finding that the right-hand side of an RMS of the first family or the left-hand side of an RMS of the second family is disturbed. The regions to have different wave patterns solved from the one-dimensional Riemann problem are displayed in the original Mach number–shock speed Mach number plane.

JFM classification

Aerodynamics: High-speed flow Compressible Flows: Shock waves

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1020 , 10 October 2025 , A5
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© The Author(s), 2025. Published by Cambridge University Press

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References

Athira, C.M., Rajesh, G., Mohanan, S. & Parthasarathy, A. 2020 Flow interactions on supersonic projectiles in transitional ballistic regimes. J. Fluid Mech. 894, A27.CrossRefGoogle Scholar
Ben-Dor, G. 2006 A state-of-the-knowledge review on pseudo-steady shock-wave reflections and their transition criteria. Shock Waves 15 (3), 277–294.10.1007/s00193-006-0036-zCrossRefGoogle Scholar
Ben-Dor, G., Igra, O. & Elperin, T. 2000 Handbook of Shock Waves. Elsevier.Google Scholar
Blankenship, V.D. 1965 Shock–shock interaction on a slender supersonic cone. J. Fluid Mech. 22 (3), 599–615.CrossRefGoogle Scholar
Brown, E.A. & Mullaney, G.J. 1965 Experiments on the head-on shock–shock interaction. AIAA J. 3 (11), 2168–2170.Google Scholar
Candler, G. 1989 On the computation of shock shapes in nonequilibrium hypersonic flows. In 27th Aerospace Sciences Meeting, pp. 312. American Institute of Aeronautics and Astronautics.Google Scholar
Das, D., Desai, S. & Kulkarni, V. 2021 Transition of shock reflection at higher enthalpies for Earth and Mars atmospheres. Acta Astronaut. 188, 289–294.10.1016/j.actaastro.2021.07.042CrossRefGoogle Scholar
Das, D., Desai, S. & Kulkarni, V. 2022 a Shock/expansion fan interaction with real gas effects for Earth and Mars atmospheric conditions. Heat Transfer 51, 5464–5480.10.1002/htj.22555CrossRefGoogle Scholar
Das, D., Desai, S., Kulkarni, V. & Gadgil, H. 2022 b Real-gas effects for shock/shock interaction in Earth and Mars atmospheres. J. Spacecr. Rockets 59 (6), 1853–1868.10.2514/1.A35142CrossRefGoogle Scholar
Edney, B. 1968 Anomalous heat transfer and pressure distributions on blunt bodies at hypersonic speeds in the presence of an impinging shock. Tech. Rep. Flygtekniska Forsoksanstalten.10.2172/4480948CrossRefGoogle Scholar
Gentry, R.A., Martin, R.E. & Daly, B.J. 1966 An Eulerian differencing method for unsteady compressible flow problems. J. Comput. Phys. 1 (1), 87–118.10.1016/0021-9991(66)90014-3CrossRefGoogle Scholar
Gnoffo, P.A., Gupta, R.N. & Shinn, J.L. 1989 Conservation Equations and Physical Models for Hypersonic Air Flows in Thermal and Chemical Nonequilibrium. National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Division.Google Scholar
Gottlieb, J.J. & Groth, C.P.T. 1988 Assessment of Riemann solvers for unsteady one-dimensional inviscid flows of perfect gases. J. Comput. Phys. 78, 437–458.10.1016/0021-9991(88)90059-9CrossRefGoogle Scholar
Gupta, R.N., Yos, J.M., Thompson, R.A. & Lee, K.-P. 1990 A review of reaction rates and thermodynamic and transport properties for an 11-species air model for chemical and thermal nonequilibrium calculations to 30000 K. NASA Reference Publication 1232.Google Scholar
Hillier, R. 2007 Shock-wave/expansion-wave interactions and the transition between regular and Mach reflection. J. Fluid Mech. 575, 399–424.10.1017/S0022112006004083CrossRefGoogle Scholar
Inger, G.R. 1966 a Blast wave impingement on a slender wedge moving at hypersonic speeds.. AIAA J. 4 (3), 428–435.CrossRefGoogle Scholar
Inger, G.R. 1966 b Oblique blast impingement on slender hypersonic bodies. AIAA J. 4 (8), 1475–1477.10.2514/3.3715CrossRefGoogle Scholar
Kudryavtsev, A.N., Khotyanovsky, D.V., Ivanov, M.S., Hadjadj, A. & Vandromme, D. 2002 Numerical investigations of transition between regular and Mach reflections caused by free-stream disturbances. Shock Waves 12 (2), 157–165.Google Scholar
Kutler, P. & Sakell, L. 1975 Three-dimensional, shock-on-shock interaction problem. AIAA J. 13 (10), 1360–1367.Google Scholar
Kutler, P., Sakell, L. & Aiello, G. 1974 On the shock-on-shock interaction problem. In 7th Fluid and PlasmaDynamics Conference, p. 524. American Institute of Aeronautics and Astronautics.Google Scholar
Kutler, P., Sakell, L. & Aiello, G. 1975 Two-dimensional shock-on-shock interaction problem. AIAA J. 13 (3), 361–367.10.2514/3.49705CrossRefGoogle Scholar
Law, C., Felthun, L.T. & Skews, B.W. 2003 Two-dimensional numerical study of planar shock-wave/moving-body interactions. Part I: Plane shock-on-shock interactions. Shock Waves 13, 381–394.10.1007/s00193-003-0218-xCrossRefGoogle Scholar
Law, C. & Skews, B.W. 2003 Two-dimensional numerical study of planar shock-wave/moving-body interactions. Part II: Non-classical shock-wave/moving-body interactions. Shock Waves 13, 395–408.Google Scholar
Li, H. & Ben-Dor, G. 1997 Analytical investigation of two-dimensional unsteady shock-on-shock interactions. J. Fluid Mech. 340, 101–128.10.1017/S0022112097005326CrossRefGoogle Scholar
Liou, M.-S. 1996 A sequel to AUSM: AUSM+. J. Comput. Phys. 129 (2), 364–382.10.1006/jcph.1996.0256CrossRefGoogle Scholar
Macheret, S.O., Losev, S.A., Chernyi, G.G. & Potapkin, B.V. 2002 Physical and Chemical Processes in Gas Dynamics: Cross Sections and Rate Constants, vol. I. American Institute of Aeronautics and Astronautics.10.2514/4.866661CrossRefGoogle Scholar
Merritt, D.L. & Aronson, P.M. 1966 Free flight shock interaction studies. AIAA paper (66-57).Google Scholar
Merritt, D.L. & Aronson, P.M. 1967 Wind Tunnel Simulation of Head-On Bow Wave–Blast Wave Interactions, United States Naval Ordnance Laboratory.Google Scholar
Park, C. 1990 Nonequilibrium Hypersonic Aerothermodynamics. Wiley.Google Scholar
Park, C. 1996 Review of Finite-Rate Chemistry Models for Air Dissociation and Ionization. Springer Netherlands.10.1007/978-94-009-0267-1_39CrossRefGoogle Scholar
Ramshaw, J.D. 1993 Hydrodynamic theory of multicomponent diffusion and thermal diffusion in multitemperature gas mixtures. J. Non-Equilib. Thermodyn. 18, 121–134.10.1515/jnet.1993.18.2.121CrossRefGoogle Scholar
Smyrl, J.L. 1963 The impact of a shock-wave on a thin two-dimensional aerofoil moving at supersonic speed. J. Fluid Mech. 15 (2), 223–240.Google Scholar
Tchuen, G., Burtschell, Y. & Zeitoun, D.E. 2011 Numerical study of the interaction of type IVr around a double-wedge in hypersonic flow. Comput. Fluids 50, 147–154.10.1016/j.compfluid.2011.07.002CrossRefGoogle Scholar
Toro, E.F. 2013 Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction. Springer Science & Business Media.Google Scholar
Wang, M. & Wu, Z. 2021 Reflection of a moving shock wave over an oblique shock wave. Chinese J. Aeronaut. 34 (5), 399–403.10.1016/j.cja.2020.12.029CrossRefGoogle Scholar
Wang, M. & Wu, Z. 2025 Reflection of a rightward-moving shock wave over a steady oblique shock with post-formed expansion wave. J. Fluid Mech. 1008, A19.CrossRefGoogle Scholar
Wang, M., Xu, Z.Z. & Wu, Z. 2024 Reflection of a rightward-moving oblique shock of first family over a steady oblique shock wave. J. Fluid Mech. 979, A28.10.1017/jfm.2023.988CrossRefGoogle Scholar
Wang, M.-M. & Wu, Z.-N. 2022 Reflection of rightward moving shocks of the first and second families over a steady oblique shock wave. J. Fluid Mech. 936, A18.10.1017/jfm.2022.53CrossRefGoogle Scholar